The operation of a DC to DC power converter having an explicitly digital control system presents a number of problems that are not encountered in conventional power converters having analog control loops. Although it is known that the use of a current mode inner control loop for a power supply is equivalent to a sampling system having a delay, with a resulting infinite number of zeroes, these effects only matter at frequencies that are approximately equal to one half of the switching frequency, i.e., at frequencies substantially above the bandwidth. Quantization of the converter pulsewidth, on the other hand, is important at all frequencies, and thus cannot be accurately modelled with an analog approximation.
Pulsewidth quantization results in unconventional converter behavior. For example, if a disturbance is introduced into the analog portion of the closed control loop, and if that disturbance is sufficiently small that it does not cause the duty cycle of the pulse width modulator (PWM) to increase by a sufficient amount, then the duty cycle generated by the digital controller will be unaffected. That is, sufficiently small disturbances can be shown to have zero gain (-.infin.dB).
A further example of unconventional behavior can be conceptualized as follows, for the case where the disturbance has an amplitude that is sufficient to perturb the control loop. Assume that an analog sinusoidal disturbance is introduced into the control loop, and then further assume that the disturbance has sufficient amplitude so that once every cycle it causes the duty cycle to increase from a first quantized step to a next, second quantized step, and then to decrease back to the first quantized step for the rest of the cycle. Since the output voltage is given by the product of the input voltage times the duty cycle, a quantized step in the output voltage will also occur once every cycle. The control loop will attempt to correct this variation in output voltage. However, the control loop cannot perform this correction at a rate faster than its bandwidth. Thus, if the disturbance frequency is greater than the closed loop bandwidth, the entire system will oscillate at that bandwidth, attempting to correct the disturbance. This type of oscillation, which is due solely to the duty cycle quantization inherent in the digital control loop, is referred to herein as a digital oscillation.
Digital oscillations can also occur if an output voltage magnitude, which is a function of the reference voltage and the input voltage (for a buck converter), is not exactly equal to one of the possible duty cycles. In this case the system will detect that the voltage is, for example, too low, and will increase the duty cycle to the next quantized step. The system will then detect that the voltage is too high, and will decrease the duty cycle back to the original step. These corrections occur cyclically at the bandwidth frequency, and thus also results in a digital oscillation.
On the other hand, as the disturbances grow sufficiently large, it is clear that the quantization of the duty cycle becomes unnoticeable, and the system is well approximated by a continuous duty cycle and conventional analog behavior, i.e., the converter system exhibits a phase and gain margin.
In summary, there are two types of stability that need to be addressed when implementing a power converter having a digital control loop, in addition to the conventional analog-type of stability. The two types of stability concerns relate to: (a) digital oscillations due to noise injection; and (b) oscillations due to a mismatch between the output voltage setpoint and the available (quantized) duty cycles. The first type of stability concern is independent of the power supply's operating point; while the second type depends on the input and output voltages, as well as on the number of possible duty cycles.
Reference may be had to U.S. Pat. Nos. 4,630,187 and 4,725,940 by C. P. Henze for teaching quantized duty ratio power converters, and to U.S. Pat. No. 5,272,614 by Brunk et al. for teaching a microprocessor-controlled DC-DC converter that outputs a switch control signal that has both coarse and fine quantization.